Consider a town in which only two residents, Kenji and Lucia, own wells that pro
ID: 1217307 • Letter: C
Question
Consider a town in which only two residents, Kenji and Lucia, own wells that produce water safe for drinking. Kenji and Lucia can pump and sell as much water as they want at no cost. For them, total revenue equals profit. The following table shows the town's demand schedule for water.
Suppose Kenji and Lucia form a cartel and behave as a monopolist. The profit-maximizing price is _______ per gallon, and the total output is ______ gallons. As part of their cartel agreement, Kenji and Lucia agree to split production equally. Therefore, Kenji's profit is, and Lucia's profit is _________.
Suppose that Kenji and Lucia have been successfully operating as a cartel. They each charge the monopoly price and sell half of the monopoly quantity. Then one night before going to sleep, Kenji says to himself, "Lucia and I aren't the best of friends anyway. If I increase my production to 35 gallons more than the cartel amount, I can increase my profit even though her profit goes down. I will do that starting tomorrow."
After Kenji implements his new plan, the price of water (increases/decreases) to_________per gallon. Given Lucia and Kenji's production levels, Kenji's profit becomes_________ and Lucia's profit becomes_________.
Because Kenji has deviated from the cartel agreement and increased his output of water to 35 gallons more than the cartel amount, Lucia decides that she will also increase her production to 35 gallons more than the cartel amount.
After Lucia increases her production, Kenji's profit becomes_________, Lucia's profit becomes_________, and total profit (the sum of the profits of Kenji and Lucia) is now_________.
Price Quantity Demanded Total Revenue (Dollars per gallon) (Gallons of water) (Dollars) 3.60 0 0 3.30 35 $115.50 3.00 70 $210.00 2.70 105 $283.50 2.40 140 $336.00 2.10 175 $367.50 1.80 210 $378.00 1.50 245 $367.50 1.20 280 $336.00 0.90 315 $283.50 0.60 350 $210.00 0.30 385 $115.50 0 420 0Explanation / Answer
Given,
Total Revenue = Profit
When Kenji and Lucia form a cartel and behave as a monopolist. The profit maximizing Price is $1.80 per gallon, and the total output is 210 gallons. ( it is so because total revenue = profit and monopoly maximize price and output is where the profit (total revenue) is maximum which is $378.00 in the table and at this level price is $1.80 and quantity is 210)
As part of their cartel agreement, Kenji and Lucia agree to split production equally. Therefore, Kenji's profit is, and Lucia's profit is $189 ( it is so because they agree to split the cartel production equally, it means now both will produce 210/2 = 105 gallons at the price $1.80 so their profits will be 105*1.80 = 189. Or simply divide the total profit of 378.00 into 2 equal parts i.e., 378/2 =$189 )
Suppose that Kenji and Lucia have been successfully operating as a cartel. They each charge the monopoly price and sell half of the monopoly quantity. Then one night before going to sleep, Kenji says to himself, "Lucia and I aren't the best of friends anyway. If I increase my production to 35 gallons more than the cartel amount, I can increase my profit even though her profit goes down. I will do that starting tomorrow."
After Kenji implements his new plan, the price of water (increases/decreases) to decrease per gallon.( It is so because when Kenji increases production to 35 gallon more than the cartel amount it means now total production is 210 + 35 = 245 and in the table price at 245 gallon is 1.50 which is less than 1.80. thats why price of water decreases). Given Lucia and Kenji's production levels, Kenji's profit becomes 140 * 1.5 = $210 and Lucia's profit becomes 105 * 1.5 = $157.5 .(it is so because now Kenji produce 105+35 = 140 units and price is now $1.50 in the market so his profit = 140*$1.50 similarly Lucia is producing same cartel decided amount that is 105 so his profit = 105*1.50 = 157.5).
Because Kenji has deviated from the cartel agreement and increased his output of water to 35 gallons more than the cartel amount, Lucia decides that she will also increase her production to 35 gallons more than the cartel amount.
After Lucia increases her production, Kenji's profit becomes 140 * 1.20 = $168 , Lucia's profit becomes 140 * 1.20 = $168 , and total profit (the sum of the profits of Kenji and Lucia) is now $168 + $168 = $336 .
(it is so because as Lucia also increases his production to 140 by increasing 35 more gallon so now the total production is 140+140 = 280 and at 280 prices are $1.20 as given in the table, so now profit of each of them is 140*$1.20 = $168. )